3289: Highway Signs
| Highway Signs |
 Title text: Highway engineers like Planck units because, like the speed of light, the energy capacity of a typical car's gas tank is 1. |
Explanation[edit]
The signs on this highway apparently state things in terms of Planck units, which express things with reference to four fundamental physical constants. These may be useful in some fields of physics, but are, in most cases, impractical for everyday purposes.
In the Planck scheme, speeds are measured in terms of the speed of light, c. In this case, the speed limit of 0.000000097 c is about 105 km/h or 65 mph.
The "Next Exit" sign displays the distance in terms of the Planck length, which is considered the shortest measurable length, equal to approximately 1.616255 × 10-35 m. (Attempts to measure shorter lengths would require particles whose quantum wavelength was smaller than the Planck length and, since short wavelengths correspond to high energy, such particles would collapse into black holes before they could be used. A black hole with such a low mass would then evaporate by Hawking radiation in a tiny fraction of a second, in a burst of radiation and particles.) 1.39 × 1039 Planck lengths is about 23 km, or 14 miles.
It would likely be impractical for drivers to count the digits in that sign at highway speeds. If the highway department were to insist on using these units, they would be more readable (but less funny) if the numbers were in scientific notation. Of course, many drivers would find that hard to understand, too.
The title text claims that highway engineers like Planck units because the energy capacity of a gas tank is 1. The Planck energy is the mass-energy equivalent of 1 Planck mass (about 21.76 micrograms), and equal to approximately 1.956 gigajoules. On average, petrol has an energy density of approximately 46 MJ/kg or 34.2 MJ/L, so a car with a fuel tank that holds 57.2 liters (15.1 gallons) has approximately 1 Planck unit of energy. While different cars have different sized fuel tanks, this is well within the typical range. Most other Planck units are many orders of magnitude outside the range people typically use, so it's an interesting coincidence that the very high speed and very low distance cancel out and create an amount commonly encountered in the real world.
Some cars' fuel gauges already use 1 to denote a tank's maximum volume: 0 means empty, then come fractions ¼, ½, and ¾, and then 1 means full. Of course, these numbers correspond to different real volume measurements between different makes of car. However, it is unclear why the units used to measure the capacity of individual gas tanks would matter to highway engineers, who are primarily concerned with things like cost, longevity and safety of the roads those vehicles drive on, not how they operate.
Systems of measurement and their advantages and disadvantages are popular discussion subjects online,[actual citation needed] though most of the discussion focuses around the various Imperial systems of measurement (such as U.S. customary units) and their enduring popularity in certain (mostly anglophone) parts of the world. This comic may be exaggerating this discourse to the point of a reductio ad absurdum, introducing units more aligned with fundamental physics constants at the cost of fewer units having quantities close to those encountered in practice (only the Planck energy, while the other Planck units are overly large or small). The system also appears to lack any derived units capable of expressing a measurement in more convenient terms. Users of other systems can choose various distance units (commonly ranging from nanometers to kilometers or "thous" to miles) to match their needs. Similarly, a somewhat usable system could be derived from the Planck system by borrowing SI unit prefixes, for example "quettakilolength" (1033 Planck lengths = 1.616255 cm) or the "nano-c" (10-9 × c = 0.2998 m/s, 1.079 km/h, or 0.6706 MPH).
Systems of measurement are a recurring topic on xkcd. 3092: Baker's Units demonstrates units which are arguably more ridiculous than the ones shown here. In 3065: Square Units, the issues with repeated unit conversion are demonstrated (similarly, in this comic, unit conversions would be necessary for most people to understand the signs). 3038: Uncanceled Units and 2292: Thermometer deal with even more unusual, but valid, units. 3164: Metric Tip presents another case of switching from one system of measurements to another.
Transcript[edit]
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This is one of 34 incomplete transcripts: |
- [Two highway signs stand along a road with mountains in the background. One wide sign reads "NEXT EXIT" above a number starting with 1,390 followed by around thirty-six zeroes (the propreantepenultimate and preantepenultimate zero are fully, the sixth-to-last is partly blocked by post of taller sign). A second, taller sign reads "Speed Limit" above the number 0.000000097.]
- [Caption below the panel:]
- Our local highway department is switching to Planck units.
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Discussion
OK, well, my local highway department is switching to Scientific Planck units. Maybe they'd be better off with Engineering Planck units, though. JohnHawkinson (talk) 03:20, 25 August 2026 (UTC)
- But "1.39×1039" would fit both. 84.2.104.152 03:56, 25 August 2026 (UTC)
65 meters per hour seems kind of slow 198.84.136.233 03:23, 25 August 2026 (UTC)
- Agreed. I tried changing m/h to mph but my edit doesn't stick. Martin (talk) 03:35, 25 August 2026 (UTC)
TIL that the energy capacity of a typical gas tank is approximately the Planck energy. I'm surprised the Planck units contain a unit so useful on a human scale, most of them are so much larger or smaller than anything we typically encounter! Paul1764 (talk) 04:55, 25 August 2026 (UTC)
It would be easier if the distance on the road sign was stated in binary 2a00:23c8:d78f:a401:c58e:2d00:6bb:bc9c (talk) 12:18, 25 August 2026 (UTC) (please sign your comments with ~~~~)
Why the strange precision with the kilometric speed limit that's not kept for mph? 0.000000097c is indeed about 29.079868426 m/s, which converts to about 104.6875 kmh (so a rounding error too!), and it's 65.04981 mph. If you round the mph to fit with existing signage, then you should round km/h too, either to 105 (a speed limit that, to my knowledge, exists only in Canada to match the 65 mph limitation in the US) or to 100 (the international standard closest to that speed; you could also round it up to the next step, which is 110).--94.73.49.125 12:50, 25 August 2026 (UTC)
Highway Unit Trivia: Delaware Route 1 is measured in miles, but exits are numbered in kilometers. Delaware Route 1 does not touch U.S. Route 1, but terminates 20 km away, leading to local confusion when people say "It's on Route One"... Which One? 158.173.67.70 15:57, 25 August 2026 (UTC)
As a German Phycisist I like this unit system as it would define the speed limit on the German Autobahm as 1.
These guys should be doing it as ratios of dimensionless physical constants instead 122.58.18.202 20:01, 25 August 2026 (UTC)
Title/Shop Glitch: This is the second strip posted since the title/shop glitch (?), where the comic's title links directly to the shop. Was there an error with the < / a > tag? 158.173.67.16 20:30, 25 August 2026 (UTC)
For those who are metrically il-liter-ate, it would be nice to include the capacity, in gallons, of a gas tank that holds one Planck energy of chemical energy. 47.150.59.231 06:22, 27 August 2026 (UTC)
- Fun fact: I added many of the metric measurements on this page, without putting any of the US Customary ones on there, because I can’t be bothered to convert. However, in every single case (also with previous comics), someone comes along eventually and does add them. It feels like English Wikipedia might be the same? Problems no other wiki in any other language has. Kleinesfilmröllchen (talk) 11:16, 1 September 2026 (UTC)
- Thanks for adding in many of the metric measurements. And yeah, I went ahead and added the gallons in myself after my complaint (shrouded in an attempt at humor) only yielded a "fix" to that section that incorrectly changed the number of liters, while still not including gallons. Ironically the wikipedia link that was already in the explanation has the correct number of liters, and hasn't been edited since before this comic went live (at the time of this comment, at least). 47.150.59.231 16:01, 1 September 2026 (UTC)
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- Thanks for adding in many of the metric measurements. And yeah, I went ahead and added the gallons in myself after my complaint (shrouded in an attempt at humor) only yielded a "fix" to that section that incorrectly changed the number of liters, while still not including gallons. Ironically the wikipedia link that was already in the explanation has the correct number of liters, and hasn't been edited since before this comic went live (at the time of this comment, at least). 47.150.59.231 16:01, 1 September 2026 (UTC)